PERT and CPM
|
PERT : Program Evaluation and Review Technique and
CPM : Critical Path Method
|
Basically, Critical Path Method and PERT ,Programmed Evaluation Review Technique are project management techniques, which have been created out of the need of Western industrial and Army establishments to the plan, schedule and control complex projects.
Drawing the CPM/PERT Network
Each activity or sub-project in a PERT or CPM Network is shows by an arrow symbol. Each activity is antedate and succeeded by an event, shows as a circle and numbered.
• History of CPM/PERT
there is Critical Path Method {CPM}
E I Due Pont de Nemours and the Company. In 1957 for construction of new chemical plant and maintenance shut-down Then Deterministic task times
Activity-on-node network construction
And Repetitive nature of jobs
Project Evaluation and Review Technique { PERT }
U S Navy in 1958 for the POLARIS missile program
Multiple task time estimates (probabilistic nature)
Activity-on? network construction
Non-repetitive jobs. R and D work
• Project Network
Use of nodes and arrows
Arrows An arrow leads from tail to head directionally
o Shows the ACTIVITY, a time waste effort that is required to perform a part of the work.
o ?Nodes A node is represented by a circle
o - Indicate EVENT, a point in time where one or more activities start and/or finish.
• Generally Network work out is the general name given to certain specific techniques which can be used for the management, planning ,directing and control of projects
• Activity
o A task or a certain amount of work required in the project
o Requires time to complete
o Represented by an arrow
• Dummy Activity
o Indicates only precedence relationships
o Does not require any time of effort
• Event
o Signals the beginning or ending of an activity
o Designates a point in time
o Represented by a circle (node)
• Network
o Shows the sequential relationships among activities using nodes and arrows
• Activity-on-node (AON)
o nodes represent activities, and arrows show precedence relationships
• Activity-on-arrow (AOA)
o arrows represent activities and nodes are events for points in time
Project Network
in the AOA Project Network for House and AON Project Network for House (3 2 0 1 3 1 1 1 1 2 4 6 7 3 5} Lay base Design house and acquire financing Order and receive materials Dummy complete work Select carpet Select paint Build house 1 3 2 2 4 3 3 1 5 1 6 1 7 1 and then Start Design house and obtain financing Order and receive materials Select paint Select carpet Lay foundations Build house Finish work
• Situations in network diagram A must complete before either B or C can start both A and B must complete before C can start both A and C must complete before either of B or D can start A must complete before B can start both A and C must complete before D can start A B C A B C D C B A A C B D Dummy
• Network example Illustration of network search of a small redesign of a product and its assort packaging. Now key question is: How long will it take to finish this project ?
• For clarity, this list is kept to a minimum by specifying only immediate relationships, that is relationships involving activities that & quota; occur near to each other in time and quota;.
• Main Questions to prepare activity network
• Is this a fair Activity?
• Is this a end Activity?
• What Activity forego this?
• What Activity pick out this?
• What Activity is coincident with this?
• CPM calculation
• Path
o A connected sequence of activities leading from the starting event to the ending event
• Critical Path
o The longest path (time); determines the project duration
• Critical Activities
o All of the activities that make up the critical path
• Forward Pass
• Earliest Start Time (ES)
o earliest time an activity can start
o ES = maximum EF of immediate predecessors
• Earliest finish time (EF)
o earliest time an activity can finish
o earliest start time plus activity time
EF= ES + t
• Latest Start Time (LS)
o Latest time an activity can start without delaying critical path time
LS= LF - t
• Latest finish time (LF)
o latest time an activity can be completed without delaying critical path time
o LS = minimum LS of immediate predecessors
Backward Pass
• CPM analysis
• Draw the CPM network
• Analyze the paths through the network
• Determine the float for each activity
o Compute the activity’s float
o float = LS - ES = LF - EF
o Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project
• Find the critical path is that the sequence of activities and events where there is no “slack” i.e.. Zero slack
o Longest path through a network
• Find the project duration is minimum project completion time
• EXAMPLE:-
|
|
The PERT (Probabilistic) Approach
The Duration of an activity is calculated using the following formula:
Te = (t0 + 4.tm +tp)/6
Where te is the Expected time, to is the Optimistic time, tm is the most probable activity time and tp is the Pessimistic time.
It is not need to go into the theory behind the formula. It is enough to understand that the weights are based on an approximation of the Beta distribution.
The Standard Deviation, which is a good quantify of the variability of each activity is found out by the rather simplified formula:
S1 = (tp-t0)/6
The Variance is the Square of the Standard Deviation.
MORE SOLUTIONS REGARDING PERT AND CPM NETWORKING
WE ALSO PROVIDE SOLUTIONS OF OPERATIONAL RESEARCH REGARDING OTHER TOPICS:-
1) Queuing Theory
2) Simulation
3) Theory of games
4) Decision Theory
5) Transportation and Transhipment problem
6) Duality and Sensitivity Analysis
7) Simplex problem |
|
